FLAC3D Theory and Background • Constitutive Models

# Isotropic Elastic Model

In this isotropic elastic (or just, elastic, for simplicity) model, strain increment (\(\Delta{\epsilon}_{ij}\)) generate stress increment (\(\Delta{\sigma}_{ij}\)) according to the linear and reversible law of Hooke:

where the Einstein summation convention applies, \({\delta}_{ij}\) is the Kroenecker delta symbol, \(\Delta e_{ij}\) is the deviatoric strain increment, and \({\alpha}_2\) is a material constant related to the bulk modulus, \(K\), and shear modulus, \(G\), as

New stress values are then obtained from the relation

Bulk modulus, K, and shear modulus, G, are related to Young’s modulus, E, and Poisson’s ratio, \(nu\), by the following equations:

or

Examples

Frequently Asked Questions

**Q**: Can this elastic model be used for water, which has a zero shear modulus?**A**: Yes, you can simulate water behavior by setting bulk modulus equal to the water bulk modulus and shear modules to 0 in the elastic model. An example of this can be found in the Hydrodynamic Pressure Acting on a Dam case study.**Q**: What is the allowable range for Poisson’s ratio?**A**: The theoretical allowable range for Poisson’s ratio is between -1 and 0.5. However, in practice, the range is typically between 0 and 0.5.

elastic Model Properties

Use the following keywords with the `zone property`

(FLAC3D) or `block zone property`

(3DEC) command to set these properties of the elastic (isotropic) model.

or

- young f
Young’s modulus, \(E\)

- poisson f
Poisson’s ratio, \(\nu\)

Notes

Only one of the two options is required to define the elasticity: bulk modulus \(K\) and shear modulus \(G\), or, Young’s modulus \(E\) and Poisson’s ratio \(\nu\). When choosing the latter, Young’s modulus \(E\) must be assigned in advance of Poisson’s ratio \(\nu\).

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